If you can find a net with an extending handle that can help because if he's far from you it will help you reach but if he's close then you can make it shorter so it won't be so awkward and cumbersome.

When I was younger I went to a day camp every summer at a local nature center, both as a camper for years and then as a volunteer counselor for two summers. We would go "scooping" where we would go to one of two natural ponds and catch tadpoles, minnows, frogs, dragonfly nymphs, water bugs, etc with nets then release them after we'd all taken turns observing them in large buckets of water. I got really good at catching things over the years & can tell you a few things I found helped me 1) preferably squat or even better lie on your stomach with your "scooping" arm over the edge. To animals below the water surface, you look like a hulking shape or looming shadow, so squatting or lying down as opposed to standing and bending minimizes this to certain extent and seems to make it easier to "sneak up" on them and catch them. If you are worried about dirt from lying on the ground, wear old clothes and bring an old towel, sheet or a big garbage bag to put under you. If lying on the ground hurts, bring several towels or sheets and fold them under you, or if you have a body pillow or cushion from a lawn chair or lounger put that underneath you and on top of the garbage bag or towel. 2) while bigger nets have their uses, I often found it easier to catch with smaller nets, the little green ones from the pet store worked really well for smaller things. The more water is displaced by the net the more the animals seem to swim away because they are scared by the disturbed water, so smaller nets can be good because they disturb a smaller amount of water. Plus because the net is smaller they seemed create less drag in the water, meaning you can scoop more quickly giving the animal less chance to escape. Smaller nets also have a smaller opening to jump out of 3) once you have the fish in your net, put your hand over the net to keep it from jumping out, and make sure your bucket or container isn't too full of water, or use a container with a lid or some other kind of covering (even plastic wrap will work in a pinch)

I suggest maybe trying to lure the fish in with food and attempting to net him that way. Depending on how deep and wide the stream is you could try getting a big piece of cardboard, plastic or wood and when you go to catch the fish temporarily block off one side of the stream where the fish is so he has less place to swim away. If you still cant get it, try going to feed it at least once a day maybe it will start to associate you with food and will get used to you and be more willing to come near you- and your net.

Well I wouldn't be able to reach down to catch him because the wall around the stream is like 6 feet high. The path to get down to the stream is really steep as well so I have to actually get in the water to catch him. I've been trying to find a net to use to no avail :/

Great idea riverotter! I never thought of that and there's a dollar store right up the road. No luck catching him again today, the water was so stirred up from the rain I could hardly see him :/ fingers crossed, the third times the charm!

So i finally managed to catch him by climbing into the stream and chasing him around and around and around until he gave up and swam into the net gracefully. So we're both very tired and I'm very cold and it's safe to say he's the creepiest thing I've ever laid eyes on. So without further ado, the swamp monster:

I do not know what your laws are but I would report this to your town. Here in Ontario we are required to report any invasive species found in our waters to Fish and Wildlife to help scientists keep track.
It might even make a cute news story/public announcement. Abandoned goldfish given a second chance/warning to not release any domestic animals into the wild.Posted via Mobile Device

Ok. I'm not sure who I'd contact but I'll look around to find a number to call

I see you are in the US, so your state Department of Natural Resources (or Department of Environment, Department of Conservation, or what ever your states environmental agency or agencies is officially called) is probably your best bet. Some states have more than one agency, while others like mine just have a Department of Natural Resources. Wikipedia has a list of each state's environmental agencies.